Least Common Multiple (LCM) of 113 and 185
The least common multiple (LCM) of 113 and 185 is 20905.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 185?
First, calculate the GCD of 113 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 185 = 0 remainder 113 |
| 2 | 185 ÷ 113 = 1 remainder 72 |
| 3 | 113 ÷ 72 = 1 remainder 41 |
| 4 | 72 ÷ 41 = 1 remainder 31 |
| 5 | 41 ÷ 31 = 1 remainder 10 |
| 6 | 31 ÷ 10 = 3 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 191 | 5921 |
| 62 and 64 | 1984 |
| 109 and 21 | 2289 |
| 179 and 92 | 16468 |
| 112 and 165 | 18480 |